objective teaching the lesson materialsellis2020.org/itlg/itlg grade 4/u8.5.pdf · area 2cm area...

Teaching the Lesson materials

Key ActivitiesStudents count squares to find the areas of rectangles and then develop a formula for the area of a rectangle. They use the formula to find the area of a rectangle whose length and/orwidth is not a whole number of units.

Key Concepts and Skills• Rename fractions as decimals. [Number and Numeration Goal 5]• Count unit squares or use a formula to find the area of a rectangle.

[Measurement and Reference Frames Goal 2]• Use patterns in a table to develop a formula for the area of a rectangle.

[Patterns, Functions, and Algebra Goal 1]• Apply the Distributive Property of Multiplication over Addition.

[Patterns, Functions, and Algebra Goal 4]

Key Vocabularylength • base • width • height • area • formula • variable

Ongoing Assessment: Informing Instruction See page 684.

Ongoing Learning & Practice materialsStudents plot and name points on a coordinate grid.

Students practice and maintain skills through Math Boxes and Study Link activities.

Ongoing Assessment: Recognizing Student Achievement Use journal page 235.[Measurement and Reference Frames Goal 2]

Differentiation Options materials

Students roll a die to determine thedimensions of arectangle. They build the rectangleand find its area.

Students find theareas of rectanglesusing thedimensions of atennis court.

Students use astring loop to findrectangles withvarious areas that all have a perimeterof 24 inches.

Students add length,width, base, andheight to their MathWord Banks.

� Teaching Masters(Math Masters,pp. 257–259)

� Teaching AidMaster (MathMasters, p. 444)

� DifferentiationHandbook

� 1 six-sided die;36 square pattern blocks;24-inch stringloop; tape

ELL SUPPORTENRICHMENTENRICHMENTREADINESS

3

� Math Journal 2, pp. 234 and 235� Study Link Master (Math Masters,

p. 256)

2

� Math Journal 2, pp. 232 and 233� Study Link 8�4� calculator� slate

See Advance Preparation

1

Objective To guide the development and use of a formula for

the area of a rectangle.

Technology Assessment Management System

Math Boxes, Problem 2See the iTLG.

Additional InformationAdvance Preparation For Part 1, draw this table on the board:

Lesson 8�5 681

Rectangle Length Width Areaof Base (height)

A

B

C

682 Unit 8 Perimeter and Area

Math Message

1. Find the area of each rectangle.

Area � cm2 Area � cm2 Area � cm2

2. Fill in the table.

3. Write a formula for the area of a rectangle.

Area �

3098

232

Areas of RectanglesLESSON

8 � 5

Date Time

I � w, or b � h

1 cm2

A B C

length(of base)

wid

th(o

r hei

ght)

134

Number of Number of Total numberRectangle squares per row rows of squares Number model

A 4 2 8 2 � 4 � 8B 3 3 9 3 � 3 � 9C 5 6 30 5 � 6 � 30

Math Journal 2, p. 232

Student Page

� Math Message Follow-Up(Math Journal 2, p. 232)

Most students will simply count the number of squares inRectangles A and B. For Rectangle C, some students may countthe number of squares in one row 5, count the number of rows 6,and multiply. 6 � 5 � 30, so the area equals 30 cm2.

Remind students how to write a number model for the area ofRectangle A: There are 2 rows with 4 squares in each row, for atotal of 8 squares. Two rows of 4 squares each is equivalent to 2 � 4 � 8 squares. Have students record this information in thetable in Problem 2 on journal page 232. They can complete thetable for Rectangles B and C on their own.

Tell students that in this lesson they will develop a formula for the area of any rectangle.

� Developing a Formula for the Area of a Rectangle(Math Journal 2, p. 232)

Draw a rectangle on the board. Choose one of the sides (forexample, the side on which the rectangle “sits”) and label it thebase. (Any side can be designated as the base.) The length of thebase of a rectangle is called either length or base, for short.

Explain that the shortest distance between the base and the sideopposite the base is called either the width or height of therectangle. Label it on the drawing. In a rectangle, the width is the length of a side adjacent to the base.

WHOLE-CLASS

ACTIVITY

WHOLE-CLASS

ACTIVITY

1 Teaching the Lesson

Getting Started

Math MessageComplete Problem 1 on journal page 232.

Study Link 8�4 Follow-Up Students share estimation strategies. One approachis to combine areas of partial squares. Some studentsmay describe a strategy in which they found the area of large rectangular regions within São Paulo State by multiplying length by width.

Ask students to share the number models they used to determinethe area in square miles.

Mental Math and ReflexesPose multiplication facts and problems. Suggestions:

6 � 7 � 424 � 8 � 327 � 9 � 638 � 6 � 489 � 4 � 36

70 � 50 � 3,50040 � 60 � 2,40080 � 60 � 4,80090 � 300 � 27,000700 � 80 � 56,000

62 � 5 � 31058 � 6 � 34849 � 8 � 3926 � 123 � 7384 � 217 � 868

233

Areas of Rectangles continuedLESSON

8 � 5

Date Time

4. Fill in the table at the bottom of the page.

D E

F

G

H I

Area (counting Length Width AreaRectangle squares) (of base) (or height) (using formula)

Dcm2 cm cm cm2

Ecm2 cm cm cm2

Fcm2 cm cm cm2

G cm2 cm cm cm2

H cm2 cm cm cm2

Icm2 cm cm cm220.254.54.520.25

17.553.542249339102.5410284728

17.5


Student Page

Lesson 8�5 683

length of base

width,or

height

Links to the Future

NOTE Since a rectangle is a special kind ofparallelogram, and the usual formula for thearea of a parallelogram is A � b � h, theauthors will most often use this form for thearea of a rectangle. However, in certain contexts, the formula A � l � w is preferable.

Adjusting the Activity

Ask students to help you fill out the following table.

Have small groups of students look at the patterns in the tableand generate a rule that could be used to find the area of anyrectangle. Ask students to share their rules.

Summary: If the length of the base and the width of a rectangleare known, the area can be found by multiplying.

Area of a rectangle � length of the base � width of the rectangle

Such a rule is called a formula. It can be abbreviated as

A � l � w

In the formula, the letter A stands for area of a rectangle, theletter l for length of the base, and the letter w for width of therectangle. Another way of writing this formula is

A � b � h

Here the letter b stands for length of the base and the letter hfor height of the rectangle.

Have students record a formula for the area of a rectangle inProblem 3 on journal page 232. Remind the class that the lettersin a formula are called variables. They can take on any value;that is, their values can vary. To support English languagelearners, write the word variable on the board and provide some examples.

The use of a formula to calculate the area of a rectangle is a Grade 5 Goal.

� Using a Formula for the Area of a Rectangle(Math Journal 2, p. 233)

Ask partners to count squares to find the areas of the rectanglesin Problem 4 on journal page 233 and to record the results in thesecond column in the table.

ELL

Have students label the base (b) and the height (h) of each rectanglebefore working on the journal page.

A U D I T O R Y � K I N E S T H E T I C � T A C T I L E � V I S U A L

PARTNER

ACTIVITY

A 4 cm 2 cm 8 cm2

B 3 cm 3 cm 9 cm2

C 5 cm 6 cm 30 cm2

Rectangle Lengthof Base

Width(height) Area


235

Math Boxes LESSON

8 � 5

Date Time

5. Complete.

a. is half as much as 44.

b. 90 is twice as much as .

c. is 3 times as much as 40.

d. 20 is �15� of .

e. is 5 times as much as 34.170100

12045

226. Divide with a paper-and-pencil algorithm.

5,682 / 4 �

1. Write three equivalent fractions for each fraction.

a. �12� , ,

b. �34� , ,

c. �23� , ,

d. �56� , ,

�5600��

2350��

1102�

�1241��1

82��

46�

�3468��1

92��

68�

�2400��1

50��

48�

3. Complete the “What’s My Rule?” table,and state the rule.

Rule: �3.36

2. Find the perimeter of this polygon.

Number model:

Perimeter � cm22

4 � 4 � 4 � 1 � 1 �

162–166

22 23179

4. If you throw a die 60 times, about howmany times would you expect to come up?

times10

Sample answers:

81

49–51

in out

3.66 7.02

0.44 3.80

8.73

9.30 12.66

4 cm

4 cm

4 cm1 cm

1 cm

1 cm

1 cm

?

�

1,420 �24�, or 1,420 �

12�

1 � 1 � 6 � 22

12.09


Student Page

234

Coordinate GridsLESSON

8 � 5

Date Time

144

1. Plot and label each point on the coordinate grid.

A (2,6)

B (5,5)

C (8,3)

D (4,2)

E (8,9)

F (2,10)

G (5,8)

H (1,4)

2. Write the ordered number pair for each point plotted on the coordinate grid.

I ( , )

J ( , )

K ( , )

L ( , )

M ( , )

N ( , )

O ( , )

P ( , )

Q ( , )

R ( , )8715299159223643

10775

10 2 3 4 5 6 7 8 9 10

1

0

2

4

3

5

6

7

8

9

10

HA

FG

E

B

DC

10 2 3 4 5 6 7 8 9 10

1

0

2

4

3

5

6

7

8

9

10

I

J

R

P

Q

L

M

K

O

N


Student PageHave students share their results. Students should note that allrectangles except D contain half-squares, and that Rectangles Gand I contain quarter-squares. Make sure that studentsunderstand how to count the partial squares. For example:

� Rectangle G—2 half-squares are the same as 1 square, and 4 quarter-squares are the same as 1 square.

� Rectangle H—5 half-squares are the same as 2�12� squares.

Next, have students record the length of the base and the height ofeach rectangle. Then have them use the formula to find the area ofa rectangle by multiplying the base times the height.

Ongoing Assessment: Informing InstructionWatch for different multiplication strategies. For example, the length of the baseof Rectangle E is 4 centimeters and the height is 2 �

12� centimeters.

� Students use the fraction keys to enter 2 �12� into their calculator or enter 2.5 as

the decimal equivalent. 2 �12� � 4 �10 or 2.5 � 4 �10

� Students use the Distributive Property of Multiplication over Addition to set upthe problem. 4 � 2 �

12� � 4 � (2 � �

12�) � (4 � 2) � (4 � �

12�) Then they use

repeated addition to multiply the fraction �12� by the whole number 4.

8 � �12� � �

12� � �

12� � �

12� � 10

� Using a Coordinate Grid(Math Journal 2, p. 234)

Students plot and label points on a coordinate grid. They write theordered number pair for each point on another grid.

� Math Boxes 8�5(Math Journal 2, p. 235)

Mixed Practice Math Boxes in this lesson are paired with Math Boxes in Lesson 8-7. The skill in Problem 6previews Unit 9 content.

Ongoing Assessment:Recognizing Student Achievement

Use Math Boxes, Problem 2 to assess students’ ability to find the perimeter of a figure. Students are making adequate progress if they are able to find thelength of the missing side and add the measurements to find the perimeter.Some students may be able to write a number model that includes parentheses. (3 � 4) � (4 � 1) � 6 � 22

[Measurement and Reference Frames Goal 2]

Math Boxes

Problem 2 �

INDEPENDENT

ACTIVITY

INDEPENDENT

ACTIVITY

2 Ongoing Learning & Practice

STUDY LINK

8�5 Areas of Rectangles

Name Date Time

Find the area of each rectangle.

1. 2.

Number model: Number model:

Area � square feet Area � square inches

3. 4.

Number model: Number model:

Area � square centimeters Area � square meters

The area of each rectangle is given. Find the missing length.

5. 6.

7. 3, 6, , 12, , , 8. 14, 21, , , 42, ,

9. 30, , 42, 48, , , 10. 12, , 36, , 60, , 8472482466605436564935282118159

3 in.

?

25 � 12 � 30024 � 36 � 864

3 � 7 � 216 � 8 � 48

Practice

Try This

8'

6'

3"

7"

48 21

36 cm

24 c

m 12 m

25 m

864 300

Area � 27 in2

height � in.9

12 c

m

?Area � 120 cm2

base � cm10

134

Math Masters, p. 256

Study Link Master

Lesson 8�5 685

� Study Link 8�5(Math Masters, p. 256)

Home Connection Students use a formula to calculateareas of rectangles.

� Finding Areas of Rectangles(Math Masters, p. 257)

To provide experience finding the area of a rectangle using a concrete model, have students build rectangles with squarepattern blocks. Ask students to discuss the pattern they see in the table they created on Math Masters, page 257.

NOTE Square pattern blocks are prisms, not 2-dimensional polygons as thename implies. For this activity, have students consider only the square face of the pattern block.

5–15 Min

PARTNER

ACTIVITYREADINESS

3 Differentiation Options

INDEPENDENT

ACTIVITY

LESSON

8�5

Name Date Time

Area of a Rectangle

134

1. Take turns rolling a die. The first roll represents the length of the base of a rectangle. The second roll represents the height of the rectangle.

2. Use square pattern blocks to build the rectangle. Count squares to find the area.

Example:

First roll 4, second roll 3

3. Record your results in the table.

4. Describe a pattern in your table.

The number in column 1 (base) � the number in column 2 (height) � the number in column 3 (area).

5. Without building the rectangle, can you use this pattern to find the area of arectangle with a base of 8 units and a height of 7 units? Explain your answer.

8 would be in the first column, 7 in the second, and8 � 7 � 56. So the area would be 56 square units.

First Roll Second Roll Area(length of base) (height) (square units)

4 3 12

base

heig

ht

Area: 12 square units

Sample answers:


Teaching Master


LESSON

8�5

Name Date Time

Perimeter and Area

131 134

1. Tape together two copies of 1-inch grid paper (Math Masters, page 444).

2. Use a 24-inch string loop to find as many different rectangles as possible that have a perimeter of 24 inches.

3. Record your results in the table.

4. Use your results to describe a relationship between the lengths of sides and areas of rectangles that have the same perimeter.

The closer the sides are in length, the larger the area.

5. What is another name for the rectangle with the largest area?

Length of Base Height Perimeter Area(in.) (in.) (in.) (in2)

11 1 24 1110 2 24 209 3 24 278 4 24 327 5 24 356 6 24 36

10 �12

� 1�12� 24 15�

34�

7�12� 4 �

12

� 24 33�34�

square


Teaching Master

LESSON

8�5

Name Date Time

The Tennis Court

Tennis can be played either by 2 people or by 4 people. When 2 people play, it is called a game of singles. When 4 people play, it is called a game of doubles.

Here is a diagram of a tennis court. The net divides the court in half.

The two alleys are used only in doubles. They are never used in singles.

1. What is the total length of a tennis court?

2. The court used in a game of doubles is 36 feet wide. Each alley is 4�

12� feet wide. What is the width of the court used in a game of singles?

3. What is the area of a singles court?

4. What is the area of a doubles court?

5. Do you think a player needs to cover more court in a game of singles or in a game of doubles? Explain.

Sample answer: Singles game; in a singlesgame, each player covers �

12� of 2,106 sq ft,

or 1,053 sq ft. In a doubles game, each player covers of 2,808 sq ft, or 702 sq ft.

2,106 ft227 ft

78 ft

Area of rectangle � length º width

length = ?

Net

Alley

Service

Courts

Service

Courts

Alley

18 feet 21 feet

Back Court Back Court

4 feet

36 fe

et

12

134

2,808 ft2

�14�


Teaching Master

� Finding the Area of a Tennis Court(Math Masters, p. 258)

To apply students’ understanding of the formula for the area of arectangle, have them solve problems involving the dimensions of a tennis court.

� Exploring the Relationship between the Perimeter and Area of a Rectangle(Math Masters, pp. 259 and 444)

To apply students’ understanding of perimeter and area, have them use a 24-inch string loop and 1-inch grid paper toinvestigate the relationship between the perimeter and area of a rectangle.

� Building a Math Word Bank(Differentiation Handbook)

To provide language support for area, have students use the Word Bank Template found in the Differentiation Handbook. Askstudents to write the terms length, width, base, and height, drawpictures relating to each term, and write other related words. Seethe Differentiation Handbook for more information.

5–15 Min

SMALL-GROUP

ACTIVITYELL SUPPORT

15–30 Min

PARTNER

ACTIVITYENRICHMENT

5–15 Min

INDEPENDENT

ACTIVITYENRICHMENT

objective teaching the lesson materialsellis2020.org/itlg/itlg grade 4/u8.5.pdf · area 2cm area...

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